DNL 2de Maths/English
ARITHMETIC
Worksheet #20a2A definition of
Arithmetic
:
Computation using numbers and simple operations such as addition, subtraction, multiplication and division.
1. Basic symbols
= reads « equals » or « is equal to »
+ reads « plus »
– reads « minus »
× reads « multiplied by » or « times »
÷ (
or: ) reads « divided by »
Addition
a + b = c reads « a plus b equals c »
c is the sum of the two terms a and b
you add a to b , or you make an addition.
Young children are also used to saying “two and eight are ten” or “three and eight make eleven”.
Subtraction
a – b = c reads « a minus b equals c »
c is the difference between the two terms a and b
you subtract b from a , or you make a subtraction.
It is also possible to say “thirteen take away seven equals six” or “seven from thirteen leaves six”.
Multiplication
a × b = c reads « a multiplied by b equals c » or « a times b is equal to c » c is the product of the two factors a by b
you multiply a by b , or you make a multiplication.
You can also say “eight sevens are fiftysix” or “eight sevens is fiftysix” for
8×
7=
56.
Division
a : b = c or a ÷ b = c reads « a divided by b equals c »
a
b = c reads « a over b equals c »
c is the quotient of a by b ,
a is the dividend ,
b is the divisor , You divide a by b .
When you make a division in the set of natural numbers ℕ , there is often a remainder, that is the number remaining when you cannot divide a number into another an exact number of times.
Example: “4 divides into 20 five times”, therefore the remainder of the division 20 ÷ 4 is nought.
Or “you get 5 when you divide 4 into 20”.
Vocabulary: to add … to ... – addition – arithmetic – to divide … by ... – to divide (...) into ... – dividend – division – divisor – to equal – equal to – factor – to leave – multiplication – to multiply ... by ... – over – plus – product – quotient of ... by ... – remainder – to subtract ... from ... – subtraction – to take away – sum – term
2014/15 2de Worksheet #20a2 ARITHMETIC page 1/2
2. Directed numbers
Sometimes, in the set of natural numbers ℕ , it is impossible to make a subtraction (for instance
7–13).
In order to enable all subtractions, we need to use directed (whole) numbers
(or signed numbers).
The integers are 0 and all the positive or negative whole numbers. The set of integers is denoted by the capital letter ℤ . Note that 0 is neither positive, nor negative.
The opposite of
xis −
x, it reads « negative x » or « opposite x »
Example : 3 (“three” or “plus three”) is a positive integer,
whereas –9 (“minus nine” or “negative nine”) is a negative integer.
Exercises
1) What is the smallest positive integer?
What is the smallest non negative integer?
2) Make the calculations, then write them down, using only letters
a) 5–11= b) 13
–8=
c) –9–
–17=
d) –19
47=
e) –21–29=
f) −9––9=3) Read and find the solution to each equation :
a) x
50=
90 b) x –1.5=
1.7 c) 3×x=21d) 1,000x
=
100 e) x÷
5=
124) Identify the dividend, divisor, quotient and remainder in the following divisions:
a) 113 b) 12111 c) 477
d) 10199 e) 17013 f) 66677
5) Complete and read the equalities:
a) 1.5
3 = b) 1.5
3.55
=
c) −1×−1=d) 5
×−
4
7×−
2=
e)
2x×−
4=
f) −3×−5x=6) Read and work out the algebraic sums and say if they are positive or negative numbers:
(i) S
=
5–7
3–3.5–0.3 (ii) S '=
50.5–15
4–20.5 (iii) S' '=−1,000.051,005–1,000.51.000 53. Order of operation
The order of operation for integers is the same as for natural numbers :
B rackets, E xponents, M ultiplication and D ivision, A ddition and S ubtraction
The memory aid for the order of operations is : BEMDAS
Vocabulary: BEMDAS – directed numbers – minus – negative – opposite – positive – signed numbers
2014/15 2de Worksheet #20a2 ARITHMETIC page 2/2
